Problem: What's the first wrong statement in the proof below that $ \triangle CEB \cong \triangle CEF$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{CE} \cong \overline{AC}$ $, \ $ $ \angle ECF \cong \angle ACB$ $, \ $ $ \angle CFE \cong \angle ABC$ $, \ $ $ \overline{CF} \cong \overline{BD}$ $, \ $ $ \angle CFE \cong \angle DBE$ $, \ $ and $\ $ $ \angle CEF \cong \angle BED$ Proof $ \triangle CAB \cong \triangle CEF$ because AAS $ \overline{BC} \cong \overline{CF}$ because corresponding parts of congruent triangles are congruent $ \overline{AB} \cong \overline{AF}$ because corresponding parts of congruent triangles are congruent $ \triangle CEF \cong \triangle DEB$ because AAS $ \overline{CE} \cong \overline{DE}$ because corresponding parts of congruent triangles are congruent $ \triangle CEB \cong \triangle CEF$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{AF} \cong \overline{AB}$ is the first wrong statement.